The effort of a route is the largest absolute height difference between consecutive cells. Return the minimum effort to go from the top-left to the bottom-right cell, moving in four directions.
Before you code
A route's cost is its worst step, not the sum of its steps. The maximum along a path never decreases as the path grows, which is all Dijkstra needs.
Hints
effort[cell]starts at infinity, except 0 at the start.- Relaxing a step:
new = max(effort[u], abs(h[u] - h[v])). - Pop cells in order of effort; stop when the target is popped. Binary search on the answer plus BFS also works.
Production & complexity notes
When solving Path with minimum effort on LeetCode (medium), always state your loop or recursion invariant before writing code. Verify how your chosen data structure behaves on degenerate inputs (single-element inputs, all-duplicate keys, strictly monotonic sequences, or maximum constraint sizes up to $10^5$ elements). In production interviews, pair your implementation with an explicit time and auxiliary space complexity proof, explain why alternative brute-force approaches violate the latency budget, and trace how cache locality and memory allocation overhead affect wall-clock throughput on real hardware. Review the step-by-step memory trace in Dijkstra's algorithm to reinforce the underlying pattern.
What it practices
Dijkstra with a non-additive path cost, from Dijkstra's algorithm.